The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena

Kanoria, M and Mandal, BN and Chakrabarti, A (1999) The Wiener-Hopf solution of a class of mixed boundary value problems arising in surface water wave phenomena. In: Wave Motion, 29 (3). pp. 267-292.

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Abstract

Two mixed boundary value problems associated with two-dimensional Laplace equation, arising in the study of scattering of surface waves in deep water (or interface waves in two superposed fluids) in the linearised set up, by discontinuities in the surface (or interface) boundary conditions, are handled for solution by the aid of the Weiner-Hopf technique applied to a slightly more general differential equation to be solved under general boundary conditions and passing on to the limit in a manner so as to finally give rise to the solutions of the original problems. The first problem involves one discontinuity while the second problem involves two discontinuities. The reflection coefficient is obtained in closed form for the first problem and approximately for the second. The behaviour of the reflection coefficient for both the problems involving deep water against the incident wave number is depicted in a number of figures. It is observed that while the reflection coefficient for the first problem steadily increases with the wave number, that for the second problem exhibits oscillatory behaviour and vanishes at some discrete values of the wave number. Thus, there exist incident wave numbers for which total transmission takes place for the second problem. (C) 1999 Elsevier Science B.V. All rights reserved.

Item Type:	Journal Article
Publication:	Wave Motion
Publisher:	Elsevier Science
Additional Information:	Copyright of this article belongs to Elsevier Science.
Department/Centre:	Division of Physical & Mathematical Sciences > Mathematics Division of Physical & Mathematical Sciences > Physics
Date Deposited:	03 Aug 2011 08:20
Last Modified:	03 Aug 2011 08:20
URI:	http://eprints.iisc.ac.in/id/eprint/38897

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